7/11 WZ = x+ 8 ZX = 3x Y X.

Q: y" – 4y' + 4y = 2.x² + 4xe²" + x sin(2x)

A: Given differential equation is

Q: Solve for y at x=2: (4x^3 - 6yx^2 + 2xy^2)dx + (2yx^2 - 2x^3)dy = 0; y(1)=4

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Q: | 4z(z* + 1)* dz Calculate: 0.

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Q: 2dx J x (3(ln x)2 + 12 ln a – 15) -

A: Answer

Q: 1) S dx 9-x2 dx 2) J2y-2 x2Vx2 -2 3) dx 2 V1-x2 |3D

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Q: 1.S (3x5 – 2x – 5x – 3) dx 2.5 (y? – 1) (3+2y) dy 3.S V + 5VX³ dx

A: Dear student. Since you have posted many sub-parts, in our policy, i have answering the first…

Q: 8. (3x +y-2)dx (3x +y +4)dy = 0

A: we only solve one problem at a time so please post your question one by one.

Q: 2dx J x (3(ln x)2 + 12 In x – 15)

A: The given integral can be evaluated using the factorization and substitution technique.

Q: Q1) Find for : dx 1) y = log3(3x3 + x²)² × In(sec-1 vVx) 2 – (x² + y)² + (x – y²)² = x³ + y³

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Q: dt - 5t 4. | zv V100 – x² dx > 6.

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Q: 1. S (x¹+3x²+1) dx 2. f(x³ + x² + x−¹)dx p³ +p²+p+1 dp 3. p3 √ 2² (√z + √z-1) dz 8x³+27 -dx 2x+3 5.…

A: The objective of the question is evaluate the anti-derivative.

Q: S(8x-6)'dx i. + 4e dt -3t ii. 3t 20(3x-2) iii. xp-

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Q: *y=(2x^2+6) find dy\dx 4x\(2x^2+6) O 6x O 4x\(2x^2+7) O

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Q: 10. (x2+y)+(x+ey)dydx=0

A: We have given the equation;

Q: Find dy. y = x/9x - 7 27x - 14 dx 9x -7 27x - 14 dx 29x -7 O 27x+ 14. dx 2/9x -7 27x + 14 dx V9x -7

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Q: 1. S 3x° + 2x3+7x - 4 dx 2. Sx7 – 48z11 3. S 10t-3 + 12t-9 + 4t³ dt 5z16dz -

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Q: find general solution (x − 3y + 5)dx + (3x − 9y − 6)dy = 0

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Q: 2x(y + 1) dx – ydy = 0 when x = 0, y = -2 %3D -

A: Here differential equation is given as 2xy+1dx-ydy=0or2xy+1dx=ydy⇒2xdx=ydyy+1⇒2xdx=dy-dyy+1

Q: 5. ft² √1-1³ dt 6. J (2x+3) dx (x²+3x-6)⁹

A: Given 5. ∫t21-t33dt6. ∫2x+3dxx2+3x-69

Q: Use variation of parameters to find the general solution: x^2y''+xy'-y = ln (x)

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Q: 10) *- dy + 8, y(1) = 1 10) dx A) y = Vx + 8x - 8 В) у%3D 1 + 8x - 8 27 C) y =x + 8x + 10 D) y = +…

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Q: 1 = S V1- xV3+ x dx %3D

A: Use integration by part

Q: 7. f(x) = sech"(vi-x) 8. y = sech Inx

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Q: 9/ (4x’y² - 2xy)dx + (3xʻy* - x*)dy = o

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Q: ³₂²₁²[z³(x + y)³] dz dy dx

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Q: 1. S+1)dy y2+4

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Q: 1. [a+vPdz (1+ Vx)²dx 1 2 (x² – x) dx (x-1 3. + x)2 -d.x x2 4. x'dx x3 – 3x + 5 -dx 5. 3 2.

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Q: x- 3y – 7)dx – (2x – 4v – 8)dy= 0

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Q: Solve the problem by using Exact DE 3 1. (2 x³ x y² - 2y + 3) dx − (x² y + 2 x) dy = 0

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Q: (A) Evaluate S (3x + 6) (4\/¤ +1) dæ. dy if dx 3x2 (B) Find 2 5 y = = (- 5 + 2x – when x = 1

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (2t – 3)·e -t²+3t dt 3 2/Inx dx . X (2у-3)12

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Q: 3 メ=3tL 2. dt 2. dyt d x

A: x and y are function of t we have to find out the first derivative and second derivative for the…

Q: Integrate x2 e a) S- 2x -d.x 2 b) S- -

A: By using integration property, we calculate the following Integral.

Q: (x + 1)2 + y = Inx; y(1) = 4 dx Oyx + 1) = xlnx – x + 9 Oyx + 1) = xlnx – x + 8 Oyx + 1) = xlnx – x…

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Q: 2X+1 1) y-vX: zx+\ X { X-4

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 7. y= (x '+1) 4x 8. y=- Vx+1 x+3 9. h(x)%D r+2x

A: Chain rule of derivative: If f and g both are differentiable function of x, then we have d/dx…

Q: Z eXZ 4. xyz dydx dz

A: Solution:

Q: x+1 2)y = ln Vx-2

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Q: 4e-2t 6] d - x(0)= 1; y(0)=1 dt 1 8t x(1)=?

A: From the given matrix equations, we get:Given:A=-1210b(t)= 4e-2t-6 8t x0=1; y0=1To find: x1=?

Q: dy dz 2. x+1 y+1 z+1

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Q: 1. y = 3x2 - 5x when x = 3 dx when x= 2 b. dt a. 32 dt dy dt

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: What integrating factor should be used to find the solution of the equation ydx + (xy + x- 3y) dy =…

A: Given that: ydx+(xy+x-3y)dy=0

Q: Q1) Find 2/3 dx a) Jas x*/9x² – 1 V2/3

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Use integrating factors to solve (x² + y² + x)dx + xydy = 0.

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Q: .3 2х+x-1 4. J dx х3+x2—4х-4

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Q: For (3x – 5x) V2x+1 find dy/dx at x-0

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Q: 2x(y+ 1) dx – ydy = 0 when x = 0, y = -2

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Q: f(x, y) = 2+ 24.xy + ln(1+ 9x² + 18y²)

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